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Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is…
In this paper we study the reconstruction of moving object densities from undersampled dynamic X-ray tomography in two dimensions. A particular motivation of this study is to use realistic measurement protocols for practical applications,…
Diffusion models have become a central tool in deep generative modeling, but standard formulations rely on a single network and a single diffusion schedule to transform a simple prior, typically a standard normal distribution, into the…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…
The standard smooth electrical resistivity tomography inversion produces an estimate of subsurface conductivity that has blurred boundaries, damped magnitudes, and often contains inversion artifacts. In many problems the expected…
The rotation robustness property has drawn much attention to point cloud analysis, whereas it still poses a critical challenge in 3D object detection. When subjected to arbitrary rotation, most existing detectors fail to produce expected…
The restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
Diffusion magnetic resonance imaging (dMRI) is an emerging medical technique used for describing water diffusion in an organic tissue. Typically, rank-2 tensors quantify this diffusion. From this quantification, it is possible to calculate…
This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where…
The use of local detectors and descriptors in typical computer vision pipelines work well until variations in viewpoint and appearance change become extreme. Past research in this area has typically focused on one of two approaches to this…
The most unique advantage of multipass SAR interferometry (InSAR) is the retrieval of long term geophysical parameters, e.g. linear deformation rates, over large areas. Recently, an object-based multipass InSAR framework has been proposed…
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…
An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth…
We present RopeTP, a novel framework that combines Robust pose estimation with a diffusion Trajectory Prior to reconstruct global human motion from videos. At the heart of RopeTP is a hierarchical attention mechanism that significantly…
General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…